Spread 1/2 TBS mayonnaise on one side of each slice of bread.
In a frying pan over medium heat, melt just enough butter to cover the bottom of the pan.
Layer the sandwich in the pan, bread (mayonnaise side up), tomato slices, mozzarella cheese, salt and pepper, basil, and the top piece of bread (mayonnaise side down).
Cook slowly over medium to medium-low heat for 3-5 minutes per side until golden and crispy.
Slice and serve immediately.